In our pending application Ser. No. 769,460, filed Feb. 17, 1977, there are disclosed several forms of reinforcing elements designed to be assembled to an innerspring assembly for the purpose of firming up the assembly, such devices being adapted to be built into the assembly at the time of manufacturing the assembly, or to be added to an already manufactured assembly to tailor the stiffness of the assembly to a customer's specification. The stiffening device which comprises the subject matter of this application constitutes an alternative form of structure designed for the same purposes as those shown in the aforesaid pending application.